yes welding transformers have overtemperature shutdown. Microwave ovens are usually restricted to ON times of 30s to 30m.

Those are not good examples of how we should treat 24hr7d operation in domestic listening.

Many welders do not have over temperature shutdown, they should but cooked industrial welder transformers are rare. 30 minutes is enough time for a small force cooled transformer such as an MOT to reach thermal equilibrium, force cooled devices reach thermal equilibrium faster than convection cooled ones

I would hardly call domestic listening 24/7, the OP has a class AB amplifier which is only likely to have the volume cranked up some of the time. They can easily measure the winding temperature by methods posted previously just to remove any doubt.

As for heat the two common winding wires used in modern transformers are Class F 155C class H 180C. While I would not like a transformer running at this temperature for loss reasons they can run at 100C reliably.